Work

Local Hamilton Type Gradient Estimates for Nonlinear Parabolic Equations on Riemannian Manifolds

Year: 2024

Type: article

Abstract: In this paper, we present a new proof and attain some new local Hamilton type gradient estimates for positive solutions to the parabolic equation $$\begin{aligned} u_{t}=\Delta _{V}u^p+au\log u+bu \end{aligned}$$ on a complete noncompact Riemannian manifold with k-Bakry-Émery Ricci curvature bounded from below, where p, a and b are some given constants. As applications, related local Hamilton type gradient estimates, some parabolic type Liouville theorems and Harnack inequalities for porous media type equation and fast diffusion type equation are established. Some known results were generalized by our results.

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-024-00248-3

Authors: Xiaosheng Li, Canfang Duan, Cheng Jin, Fanqi Zeng

Institution: Xinyang Normal University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,390